Recently, several primal–dual first-order methods have been proposed for
the three-term problem (REF ):
the Condat–Vũ algorithm [1]}, [2]}, [3]},
the primal–dual three-operator (PD3O) algorithm [4]}, and
the primal–dual Davis–Yin (PDDY) algorithm [5]}.
Algorithms for some special cases of (REF ) are also of interest.
These include the Chambolle–Pock algorithm, also known as the
primal–dual hybrid gradient (PDHG) method [6]}, [7]}
(when \(h=0\) ),
the Loris–Verhoeven algorithm [8]}, [9]}, [10]} (when \(f=0\) ),
the proximal gradient algorithm (when \(g=0\) ), and
the Davis–Yin splitting algorithm [11]} (when \(A=I\) ).
All these methods handle the nonsmooth functions \(f\)  and \(g\) 
via the standard Euclidean proximal operator.
